JIRA can be configured to allow users to create issues without having logged into JIRA. There are two related actions:

Allowing users to browse and search issues in the project without logging in.

Allowing users to create issues in that project without logging in.

These can be achieved by adding the Anyone group to the Browse Project and Create Issue permissions in the permission scheme for the project. Additionally, Reporter, in the project's field configuration scheme, must be set as optional.

Any issue created by a user who is not logged in will display 'Anonymous' for the reporter of the issue.